Commit 516c8b6
feat(Analysis/Normed/Module/WeakDual): register bornology and boundedness API (leanprover-community#36332)
## Description
This PR registers `Bornology` instance and introduces a boundedness API as discussed [on Zulip](https://leanprover.zulipchat.com/#narrow/channel/287929-mathlib4/topic/instBornology.20for.20WeakSpace.20and.20WeakDual/with/577457935).
### Main additions
- **`WeakDual.instBornology`**: Bornology instance on `WeakDual 𝕜 E` inherited from `StrongDual 𝕜 E` via `inferInstanceAs`. This makes `IsBounded` available directly on weak dual sets, where boundedness means operator-norm boundedness.
- **`isBounded_iff_isVonNBounded`**: For normed spaces over `ℝ` or `ℂ`, norm-boundedness and weak-* von Neumann boundedness coincide (via Banach–Steinhaus).
- **`isBounded_polar`** and **`isBounded_closedBall`**: Standalone lemmas replacing repeated inline `isBounded_toStrongDual_preimage_iff_isBounded.mpr ...` patterns.
- **Simp lemmas**: `isBounded_toStrongDual_preimage_iff_isBounded` and `isBounded_toWeakDual_preimage_iff_isBounded` for translating between weak and strong dual boundedness.
### API simplification
The existing lemmas `isClosed_image_coe_of_bounded_of_closed`, `isCompact_of_bounded_of_closed`, and `isSeqCompact_of_isBounded_of_isClosed` now take `IsBounded s` directly instead of the more verbose `IsBounded (StrongDual.toWeakDual ⁻¹' s)`, since the two are definitionally equal with the new bornology instance.
### Minor changes
- Replaced `grind` tactic usage with explicit term
- Fixed deprecation dates from 2024-11-19 to 2025-11-19
- Renamed local variable `F` to `E` for consistency with the rest of the file
- Added comprehensive module and declaration docstrings1 parent e077241 commit 516c8b6
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